Sourdough Strata With Tomatoes and Greens

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8 plum tomatoes, quartered lengthwise

1 tablespoon chopped fresh thyme

2 tablespoons extra-virgin olive oil

Kosher salt and freshly ground black pepper

3 cups whole milk

8 large eggs

10 ounces Italian fontina cheese, grated (about 3 cups)

1 cup grated parmesan cheese

1/4 teaspoon cayenne pepper

1 1-pound loaf sourdough bread, cut into 1-inch cubes (about 8 cups)

4 cups chopped greens, such as kale, spinach or arugula